What should the main panel breaker size be to control a 60amp GFCI for a hot tub and a 15amp GFCI outlet. The gfci's are mounted in a box that will be wired to the main panel.
The breaker feeding the sub-panel must be sized not exceed the rating of the sub-panel. So, if you install a 60 amp sub panel you can't protect it (fuse it) any higher than 60 amps. Ditto for 100 amps.
The conductors should be sized large enough to carry the load of the sub-panel and be protected by whatever breaker they are attached to.
If you have a panel like this one spa disconnect 125A that has a 60A GFCI additional spaces for the convenience outlets you would size your main breaker at least 60 depending on the draw of the tub. I usually upsize a bit in case I want to add additional lighting, or fountains in the future. The max of this model from home depot 125A but it has the 60 GFCI and provisions for additional like you asked.
The Main breaker can be equal or greater than 60 Amps, but not smaller. If you are actually referring to the breaker feeding the hot tub and not the main breaker, then that breaker needs to rated for what the manufacture requires. If it calls for a 60 Amp circuit then the wire size needs to be at least a #6.